Estimating the Expectation

A measurement follows the normal distribution with a standard deviation of 15 and an unknown expectation . You can consider that measurement to be the "original" distribution.Two statisticians propose two distinct ways to estimate the unknown quantity with the aid of a sample of size 36.They will do that by evaluating two different SAMPLING DISTRIBUTIONS to determine which method is better. There are two statisticians involved in this task: statistician "A" and statistician "B." Statistician A proposes to use the sampling distribution of the sample average as an estimate. Statistician B proposes to use the sampling distribution of the sample median instead. In order to choose between the two options they agree to prefer the statistic that has a smaller variance (with respect to the sampling distribution). Tasks 1-9 refer to this problem of comparing the two statistics to each other.

a)Assume that the actual expectation of the measurement is equal to 5 (=5). Then the expectation of the statistic that was proposed by Statistician A is equal to:_______

b)Assume that the actual expectation of the measurement is equal to 5 (=5). Then the standard deviation of the statistic that was proposed by Statistician A is equal to:_____

c)Assume that the actual expectation of the measurement is equal to 5 (=5). Then the expectation of the statistic that was proposed by Statistician B is equal to: (In order to answer this question you may need to conduct a simulation, similar to the simulations that are presented in the book. Choose the option closest to the outcome of the simulation.)____

d)Assume that the actual expectation of the measurement is equal to 5 (=5). Then the standard deviation of the statistic that was proposed by Statistician B is equal to: (In order to answer this question you may need to conduct a simulation, similar to the simulations that are presented in the book. Choose the option closest to the outcome of the simulation.)_____

Please kindly provide detailed explanation and workings, thank you.